Discrete math question. Please provide full calculations/explanations. In the fa

Question

Discrete math question. Please provide full calculations/explanations.

In the fall term of 2015, Nick^2 took COMP 2804. Nick was always sitting in the back of the classroom and spent most of his time eating bananas. Nick uses the following banana-buying-scheme: At the start of week 0, there are 2 bananas in Nick's fridge. For any integer n greaterthanorequalto 0, Nick does the following during week n: At the start of week n, Nick determines the number of bananas in his fridge and stores this number in a variable x. Nick goes to Jim's Banana Empire, buys x bananas, and puts them in his fridge. Nick takes n + 1 bananas out of his fridge and eats them during week n. For any integer n greaterthanorequalto 0, let B(n) be the number of bananas in Nick's fridge at the start of week n. Determine the value of B(n).

Explanation / Answer

Week 0 : 2 bananas initially

x = 2 => 2 more bananas bought and kept in the fridge . Total =4

1 banana will eat in the week , left banana in the fridge =3

week 1: 3 bananas initially

x = 3 => 3 more bananas bought and kept in the fridge . Total = 6

2 banana will eat in the week , left banana in the fridge = 4

week 2: 4 bananas initially

x = 4 => 4 more bananas bought and kept in the fridge . Total = 8

3 banana will eat in the week , left banana in the fridge = 5

week 3: 5 bananas initially

x = 5 => 5 more bananas bought and kept in the fridge . Total = 10

4 banana will eat in the week , left banana in the fridge = 6

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week 0 : 2

week 1 : 3

week 2 : 4

week 3 : 5

week n : n+2

From the above pattern it is clear that B(n) = n+2.

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